Three parallel algorithms for classical molecular dynamics are presented. The first assigns each processor a fixed subset of atoms; the second assigns each a fixed subset of inter-atomic forces to compute; the third assigns each a fixed spatial region. The algorithms are suitable for molecular dynamics models which can be difficult to parallelize efficiently—those with short-range forces where the neighbors of each atom change rapidly. They can be implemented on any distributed-memory parallel machine which allows for message-passing of data between independently executing processors. The algorithms are tested on a standard Lennard-Jones benchmark problem for system sizes ranging from 500 to 100,000,000 atoms on several parallel supercomputers--the nCUBE 2, Intel iPSC/860 and Paragon, and Cray T3D. Comparing the results to the fastest reported vectorized Cray Y-MP and C90 algorithm shows that the current generation of parallel machines is competitive with conventional vector supercomputers even for small problems. For large problems, the spatial algorithm achieves parallel efficiencies of 90% and a 1840-node Intel Paragon performs up to 165 faster than a single Cray C9O processor. Trade-offs between the three algorithms and guidelines for adapting them to more complex molecular dynamics simulations are also discussed.

Fast parallel algorithms for short-range molecular dynamics

Natural structural materials are built at ambient temperature from a fairly limited selection of components. They usually comprise hard and soft phases arranged in complex hierarchical architectures, with characteristic dimensions spanning from the nanoscale to the macroscale. The resulting materials are lightweight and often display unique combinations of strength and toughness, but have proven difficult to mimic synthetically. Here, we review the common design motifs of a range of natural structural materials, and discuss the difficulties associated with the design and fabrication of synthetic structures that mimic the structural and mechanical characteristics of their natural counterparts.

Bioinspired structural materials

Nature’s hierarchical materials

Biological materials: Structure and mechanical properties

Double-network (DN) gels have drawn much attention as an innovative material having both high water content (ca. 90 wt%) and high mechanical strength and toughness. DN gels are characterized by a special network structure consisting of two types of polymer components with opposite physical natures: the minor component is abundantly cross-linked polyelectrolytes (rigid skeleton) and the major component comprises of poorly cross-linked neutral polymers (ductile substance). The former and the latter components are referred to as the first network and the second network, respectively, since the synthesis should be done in this order to realize high mechanical strength. For DN gels synthesized under suitable conditions (choice of polymers, feed compositions, atmosphere for reaction, etc.), they possess hardness (elastic modulus of 0.1–1.0 MPa), strength (failure tensile nominal stress 1–10 MPa, strain 1000–2000%; failure compressive nominal stress 20–60 MPa, strain 90–95%), and toughness (tearing fracture energy of 100∼1000 J m−2). These excellent mechanical performances are comparable to that of rubbers and soft load-bearing bio-tissues. The mechanical behaviors of DN gels are inconsistent with general mechanisms that enhance the toughness of soft polymeric materials. Thus, DN gels present an interesting and challenging problem in polymer mechanics. Extensive experimental and theoretical studies have shown that the toughening of DN gel is based on a local yielding mechanism, which has some common features with other brittle and ductile nano-composite materials, such as bones and dentins.

Why are double network hydrogels so tough

Natural materials such as bone, tooth, and nacre are nanocomposites of proteins and minerals with superior strength. Why is the nanometer scale so important to such materials? Can we learn from this to produce superior nanomaterials in the laboratory? These questions motivate the present study where we show that the nanocomposites in nature exhibit a generic mechanical structure in which the nanometer size of mineral particles is selected to ensure optimum strength and maximum tolerance of flaws (robustness). We further show that the widely used engineering concept of stress concentration at flaws is no longer valid for nanomaterial design.

https://www.pnas.org/content/pnas/100/10/5597.full.pdf

Materials become insensitive to flaws at nanoscale: lessons from nature.

Natural biological materials such as bone, teeth and nacre are nanocomposites of protein and mineral with superior strength. It is quite a marvel that nature produces hard and tough materials out of protein as soft as human skin and mineral as brittle as classroom chalk. What are the secrets of nature? Can we learn from this to produce bio-inspired materials in the laboratory? These questions have motivated us to investigate the mechanics of protein–mineral nanocomposite structure. Large aspect ratios and a staggered alignment of mineral platelets are found to be the key factors contributing to the large stiffness of biomaterials. A tension–shear chain (TSC) model of biological nanostructure reveals that the strength of biomaterials hinges upon optimizing the tensile strength of the mineral crystals. As the size of the mineral crystals is reduced to nanoscale, they become insensitive to flaws with strength approaching the theoretical strength of atomic bonds. The optimized tensile strength of mineral crystals thus allows a large amount of fracture energy to be dissipated in protein via shear deformation and consequently enhances the fracture toughness of biocomposites. We derive viscoelastic properties of the protein–mineral nanostructure and show that the toughness of biocomposite can be further enhanced by the viscoelastic properties of protein.

Mechanical properties of nanostructure of biological materials

Water-repellent biological systems such as lotus leaves and water strider's legs exhibit two-level hierarchical surface structures with the smallest characteristic size on the order of a few hundreds nanometers. Here we show that such nano to micro structural hierarchy is crucial for a superhydrophobic and water-repellent surface. The first level structure at the scale of a few hundred nanometers allows the surface to sustain the highest pressure found in the natural environment of plants and insects in order to maintain a stable Cassie state. The second level structure leads to dramatic reduction in contact area, hence minimizing adhesion between water and the solid surface. The two level hierarchy further stabilizes the superhydrophobic state by enlarging the energy difference between the Cassie and the Wenzel states. The stability of Cassie state at the nanostructural scale also allows the higher level structures to restore superhydrophobicity easily after the impact of a rainfall.

Nano to micro structural hierarchy is crucial for stable superhydrophobic and water-repellent surfaces.

Biological nanocomposites, such as bone, tooth, shell, and wood, exhibit exceptional mechanical properties. Much recent effort has been directed at exploring the basic mechanical principles behind the microstructures of these natural materials to provide guidelines for the development of novel man-made nanocomposites. This article reviews some of the recent studies on mechanical properties of biological nanocomposites, including their stiffness, strength, toughness, interface properties, and elastic stability. The discussion is focused on the mechanical principles of biological nanocomposites, including the generic nanostructure of hard-mineral crystals embedded in a soft protein matrix, the flaw-tolerant design of the hard phase, the role of the soft matrix, the hybrid interface between protein and mineral, and the structural hierarchy. The review concludes with some discussion of and outlook on the development of biomimicking synthetic materials guided by the principles found in biological nanocomposites.

Mechanical Principles of Biological Nanocomposites

As organic–inorganic hybrid composites, natural biological materials exhibit superior mechanical properties such as toughness and strength in comparison with their constituent phases: the organic phase is usually very soft and the inorganic phase very brittle. Understanding the mechanisms by which nature designs strong composites with weak materials could provide helpful insight and guidance for the development and synthesis of novel materials for industrial applications. In our recent studies on nanostructure of biological materials (Proc. Natl. Acad. Sci. U.S.A. 100 (2003) 5597; Eng. Fract. Mech. 70 (2003) 1777), the nanometer size of mineral platelets is interpreted as a result of strength optimization, in that an intrinsically brittle material reaches the theoretical strength at the nanoscale despite of crack-like flaws. The mineral nanoparticles are embedded in a soft protein matrix, resulting in an organic–inorganic composite with high toughness and strength. The present study is focused on the effects of protein and protein–mineral interface. A Virtual-Internal-Bond (VIB) model, which incorporates an atomic cohesive force law into the constitutive model of materials, is adapted to model deformation and failure in the nanostructured biocomposite. We show that the protein layer can effectively enhance the toughness of biocomposites through crack shielding and impact protection.

Baohua Ji

Papers

Materials become insensitive to flaws at nanoscale: lessons from nature.

Mechanical properties of nanostructure of biological materials

Nano to micro structural hierarchy is crucial for stable superhydrophobic and water-repellent surfaces.

Mechanical Principles of Biological Nanocomposites

A study of fracture mechanisms in biological nano-composites via the virtual internal bond model